Graphical representations of an algebraic structure is always a fascinating research topic. The most well-known class of graphs is the Cayley graphs of finitely generated groups, which has been studied for a long time. Recently, some other graphical representations of groups have also been gathering more attention from researchers. Around 2000, the concept of a directed power graph was introduced by Kelarev and Quinn [1]} as a new kinds of graphical representations, and later on Chakrabarty et al. [2]} introduced the undirected power graph of a group.
